this one is difficult
a ladder 10 ft long rests against a vertical wall. if the bottom of the ladder slides away from the wall at a speed of 2 ft/s how fast is the angle between the top of the ladder and the wall changing when the angle is pi/4 radians?
I might be wrong but I think this is right.
If you think of the angle the only thing way of measuring it is by the hypotenuse. So cosine is useful, but how do you find the adjacent side?
well the hypotenuse = 10
the adjacent side is some value let's say C plus it's growing by 2ft/sec. So mathematically that means:
aka:
so then:
So now you want to see how much the angle theta is changing as time goes by, so you take the derivative in terms of t.
Can you take it from there?